Necessary and sufficient conditions for convergence of stochastic approximation algorithms under arbitrary disturbances

Author

Kulkarni, Sanjeev R. ; Horn, Charlie S.

Author_Institution

Dept. of Electr. Eng., Princeton Univ., NJ, USA

Volume

4

fYear

1995

fDate

13-15 Dec 1995

Firstpage

3843

Abstract

A parameterised extension of the Kushner-Clark condition (1978) is introduced for the study of convergence of stochastic approximation algorithms. Our results provide necessary and sufficient conditions for convergence that hold in a Hilbert space setting and apply to general gain sequences. These results exhibit the interplay among the noise sequence, the gain sequence, and key properties of the underlying function. The proof is direct, completely deterministic, and is elementary, involving only basic notions of convergence. Some corollaries to our main result are also presented

Keywords

Hilbert spaces; approximation theory; convergence; poles and zeros; Hilbert space; arbitrary disturbances; convergence; general gain sequences; necessary and sufficient conditions; noise sequence; stochastic approximation algorithm convergence; Approximation algorithms; Convergence; Equations; Extraterrestrial measurements; Hilbert space; Noise measurement; Stochastic processes; Stochastic resonance; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

0-7803-2685-7

Type

conf

DOI

10.1109/CDC.1995.479197

Filename

479197